Our effective field theory provides a general framework in which the holographic dark energy model can be tested. For instance, the non-vanishing mass of the gravitational waves, which is small at late time epoch but sizeable during the early universe, leads to a modified stochastic gravitational waves background. On the other hand, the existence of the scalar graviton whose Compton wavelength is about the size of the Hubble radius (up to an order \(\mathcal {O}(1)\sim \mathcal {O}(10)\)  coefficient) during inflation may be tested by the cosmological collider physics [1]}. It is also very intriguing to ask what would happen if the Stueckelberg field, say the time like one \(\varphi \) , couples to the standard model fields. Our EFT framework also provides a general setup where the perturbation theory of the holographic dark energy can be developed, which allows us to investigate its impacts on the cosmological structure formation in detail. All these possibilities warrant further scrutiny.
